Finite Group Databasebeta

← C103×#25382 #39930657

Subgroups — C103×#25382 #39930657

Order 26368.

980 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#497×C103C211yesmaximal, characteristic
2C2×#464×C103C211yesmaximal, characteristic
3C2×#462×C103C211yesmaximal, characteristic, complemented
4C2×#461×C103C211yesmaximal, characteristic
5C103×#2546C211yesmaximal, characteristic, complemented
6C103×#2367C211yesmaximal, characteristic
7C103×#2056C211yesmaximal, characteristic, complemented
8C103×#2055C211yesmaximal, characteristic
9C103×#2016C211yesmaximal, characteristic, complemented
10C103×#2013C211yesmaximal, characteristic
11C103×#1981C211yesmaximal, characteristic, complemented
12C103×#1940C211yesmaximal, characteristic, complemented
13C103×#1878C211yesmaximal, characteristic, complemented
14C103×#1877C211yesmaximal, characteristic
15C103×#1763C211yesmaximal, characteristic, complemented
16C22×Q16×C103C2211yescharacteristic
17C22×Q16×C103C2211yescharacteristic
18C22×Q16×C103C2211yescharacteristic
19C22×SD16×C103C2211yescharacteristic
20C22×SD16×C103C2211yescharacteristic
21C22×SD16×C103C2211yescharacteristic
22C2×C4⋊Q8×C103C2211yescharacteristic
23C2×C4⋊Q8×C103C2211yescharacteristic
24C2×C4⋊Q8×C103C2211yescharacteristic
25C2×#124×C103C2211yescharacteristic
26C2×C4×Q8×C103C2211yescharacteristic
27C2×C4×Q8×C103C2211yescharacteristic
28C2×C4×D4×C103C2211yescharacteristic
29#497×C103—24no—
30#464×C103—24no—
31#462×C103—24no—
32#461×C103—24no—
33C2×C4⋊C8×C103C2211yescharacteristic
34C2×C4⋊C8×C103C2211yescharacteristic
35C2×C4⋊C8×C103C2211yescharacteristic
36C2×#103×C103C2211yescharacteristic
37C2×#103×C103C2211yescharacteristic
38C2×#103×C103C2211yescharacteristic
39C2×#103×C103C2211yescharacteristic
40C2×#103×C103C2211yescharacteristic
41C2×#103×C103C2211yescharacteristic
42C2×#103×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#97×C103C2211yescharacteristic
45#398×C103—21no—
46#398×C103—21no—
47#391×C103C2211yescharacteristic
48#391×C103C2211yescharacteristic
49#391×C103C2211yescharacteristic
50#390×C103C2211yescharacteristic
51#389×C103—21no—
52#389×C103—21no—
53#388×C103—21no—
54#388×C103—21no—
55#385×C103—21no—
56C4×C4⋊C4×C103C2211yescharacteristic
57C4×C4⋊C4×C103C2211yescharacteristic
58C4×C22⋊C4×C103—21no—
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61#336×C103C2211yescharacteristic
62#336×C103C2211yescharacteristic
63C22×Q8×C103C2311yescharacteristic
64C22×Q8×C103C2311yescharacteristic
65C22×Q8×C103C2311yescharacteristic
66C22×Q8×C103C2311yescharacteristic
67C22×D4×C103C2311yescharacteristic
68C23×C4×C103—21no—
69C2×Q16×C103—22no—
70C2×Q16×C103—22no—
71C2×Q16×C103—22no—
72C2×Q16×C103—22no—
73C2×Q16×C103—22no—
74C2×Q16×C103—22no—
75C2×Q16×C103—41no—
76C2×Q16×C103—41no—
77C2×Q16×C103—41no—
78C2×SD16×C103—22no—
79C2×SD16×C103—22no—
80C2×SD16×C103—22no—
81C2×SD16×C103—22no—
82C2×SD16×C103—22no—
83C2×SD16×C103—22no—
84C2×SD16×C103—41no—
85C2×SD16×C103—41no—
86C2×SD16×C103—41no—
87C22×C8×C103C2311yescharacteristic
88C22×C8×C103C2311yescharacteristic
89C22×C8×C103C2311yescharacteristic
90C22×C8×C103C2311yescharacteristic
91C4⋊Q8×C103—22no—
92C4⋊Q8×C103—22no—
93C4⋊Q8×C103—22no—
94C4⋊Q8×C103—22no—
95C4⋊Q8×C103—41no—
96C4⋊Q8×C103—41no—
97#124×C103—22no—
98#124×C103D414yes—
99C4×Q8×C103—22no—
100C4×Q8×C103—22no—
101C4×Q8×C103—22no—
102C4×Q8×C103—41no—
103C4×D4×C103—22no—
104C4×D4×C103—41no—
105C2×C4⋊C4×C103—21no—
106C2×C4⋊C4×C103—21no—
107C2×C4⋊C4×C103—21no—
108C2×C4⋊C4×C103—21no—
109C2×C4⋊C4×C103—21no—
110C2×C4⋊C4×C103—21no—
111C2×C4⋊C4×C103—21no—
112C2×C4⋊C4×C103—21no—
113C2×C4⋊C4×C103D411yescharacteristic
114C2×C4⋊C4×C103D411yescharacteristic
115C2×C4⋊C4×C103C2311yescharacteristic
116C2×C4⋊C4×C103C2311yescharacteristic
117C2×C4⋊C4×C103C2311yescharacteristic
118C2×C22⋊C4×C103—21no—
119C2×C22⋊C4×C103—21no—
120C2×C22⋊C4×C103—21no—
121C2×C22⋊C4×C103—21no—
122C2×C22⋊C4×C103—21no—
123C2×C42×C103—21no—
124C2×C42×C103—21no—
125C2×C42×C103—21no—
126C2×C42×C103C2311yescharacteristic
127C2×C42×C103C2311yescharacteristic
128C2×C42×C103C2311yescharacteristic
129C4⋊C8×C103—22no—
130C4⋊C8×C103—22no—
131C4⋊C8×C103—22no—
132#103×C103—22no—
133#103×C103—22no—
134#103×C103—22no—
135#103×C103—22no—
136#103×C103—41no—
137#103×C103—41no—
138#103×C103D414yes—
139#102×C103—22no—
140#97×C103—22no—
141#95×C103—21no—
142#95×C103—21no—
143#95×C103—21no—
144#95×C103—21no—
145#95×C103—21no—
146#95×C103—21no—
147#95×C103—21no—
148#95×C103D411yescharacteristic
149#95×C103D411yescharacteristic
150C24×C103—21no—
151C2×Q8×C103—21no—
152C2×Q8×C103—21no—
153C2×Q8×C103—21no—
154C2×Q8×C103—21no—
155C2×Q8×C103—21no—
156C2×Q8×C103—21no—
157C2×Q8×C103—21no—
158C2×Q8×C103—21no—
159C2×Q8×C103—21no—
160C2×Q8×C103—21no—
161C2×Q8×C103—21no—
162C2×Q8×C103—21no—
163C2×Q8×C103—21no—
164C2×Q8×C103—21no—
165C2×Q8×C103—21no—
166C2×Q8×C103—21no—
167C2×Q8×C103—21no—
168C2×Q8×C103—21no—
169C2×Q8×C103—21no—
170C2×Q8×C103—21no—
171C2×Q8×C103—21no—
172C2×Q8×C103—21no—
173C2×Q8×C103C2×D412yes—
174C2×Q8×C103C2×D412yes—
175C2×D4×C103—21no—
176C2×D4×C103—21no—
177C2×D4×C103—21no—
178C2×D4×C103—21no—
179C2×D4×C103—21no—
180C2×D4×C103C2×D412yes—
181C22×C4×C103—21no—
182C22×C4×C103—21no—
183C22×C4×C103—21no—
184C22×C4×C103—21no—
185C22×C4×C103—21no—
186C22×C4×C103—21no—
187C22×C4×C103—21no—
188C22×C4×C103—42no—
189C22×C4×C103—42no—
190C22×C4×C103—81no—
191C22×C4×C103C2×D411yescharacteristic
192C22×C4×C103C2×D411yescharacteristic
193C22×C4×C103C2×D411yescharacteristic
194C22×C4×C103C2×D411yescharacteristic
195C22×C4×C103C2×D411yescharacteristic
196C22×C4×C103C2×D411yescharacteristic
197C22×C4×C103C2411yescharacteristic
198Q16×C103—44no—
199Q16×C103—44no—
200Q16×C103—44no—
201SD16×C103—44no—
202SD16×C103—44no—
203SD16×C103—44no—
204C2×C8×C103—21no—
205C2×C8×C103—21no—
206C2×C8×C103—21no—
207C2×C8×C103—21no—
208C2×C8×C103—21no—
209C2×C8×C103—21no—
210C2×C8×C103—21no—
211C2×C8×C103—21no—
212C2×C8×C103—21no—
213C2×C8×C103—21no—
214C2×C8×C103C2×D412yes—
215C2×C8×C103#4112yes—
216C4⋊C4×C103—22no—
217C4⋊C4×C103—22no—
218C4⋊C4×C103—21no—
219C4⋊C4×C103—21no—
220C4⋊C4×C103—21no—
221C4⋊C4×C103—21no—
222C4⋊C4×C103—21no—
223C4⋊C4×C103—42no—
224C4⋊C4×C103—42no—
225C4⋊C4×C103—42no—
226C4⋊C4×C103—42no—
227C4⋊C4×C103—42no—
228C4⋊C4×C103—42no—
229C4⋊C4×C103—42no—
230C4⋊C4×C103—42no—
231C4⋊C4×C103C2×D412yes—
232C22⋊C4×C103—24no—
233C22⋊C4×C103—24no—
234C22⋊C4×C103—42no—
235C22⋊C4×C103—42no—
236C22⋊C4×C103—81no—
237C42×C103—21no—
238C42×C103—21no—
239C42×C103—21no—
240C42×C103—21no—
241C42×C103—42no—
242C42×C103—42no—
243C42×C103—81no—
244C42×C103C2×D412yes—
245C42×C103#4112yes—
246C23×C103—22no—
247C23×C103—41no—
248C23×C103—41no—
249C23×C103—41no—
250C23×C103—41no—
251C23×C103—41no—
252C23×C103—41no—
253C23×C103C22×D411yescharacteristic
254Q8×C103—22no—
255Q8×C103—22no—
256Q8×C103—22no—
257Q8×C103—22no—
258Q8×C103—41no—
259Q8×C103—41no—
260Q8×C103—41no—
261Q8×C103—41no—
262Q8×C103—41no—
263Q8×C103—41no—
264Q8×C103—41no—
265Q8×C103—41no—
266Q8×C103—41no—
267Q8×C103—41no—
268Q8×C103—41no—
269Q8×C103—41no—
270D4×C103—22no—
271D4×C103—22no—
272D4×C103—41no—
273D4×C103—41no—
274C2×C4×C103—21no—
275C2×C4×C103—21no—
276C2×C4×C103—21no—
277C2×C4×C103—21no—
278C2×C4×C103—21no—
279C2×C4×C103—21no—
280C2×C4×C103—21no—
281C2×C4×C103—21no—
282C2×C4×C103—22no—
283C2×C4×C103—21no—
284C2×C4×C103—21no—
285C2×C4×C103—22no—
286C2×C4×C103—22no—
287C2×C4×C103—21no—
288C2×C4×C103—21no—
289C2×C4×C103—21no—
290C2×C4×C103—21no—
291C2×C4×C103—41no—
292C2×C4×C103—41no—
293C2×C4×C103—41no—
294C2×C4×C103—41no—
295C2×C4×C103—41no—
296C2×C4×C103—41no—
297C2×C4×C103—41no—
298C2×C4×C103—41no—
299C2×C4×C103—41no—
300C2×C4×C103—41no—
301C2×C4×C103—41no—
302C2×C4×C103—41no—
303C2×C4×C103—41no—
304C2×C4×C103—41no—
305C2×C4×C103—41no—
306C2×C4×C103—41no—
307C2×C4×C103—41no—
308C2×C4×C103—41no—
309C2×C4×C103—84no—
310C2×C4×C103#12112yes—
311C2×C4×C103#12112yes—
312C2×C4×C103#13712yes—
313C2×C4×C103#13712yes—
314C2×C4×C103C22×D411yescharacteristic
315C2×C4×C103C22×D411yescharacteristic
316C2×C4×C103C2×#4111yescharacteristic
317C2×C4×C103C2×#4111yescharacteristic
318C2×C4×C103H(5,𝔽2)11yescharacteristic
319C2×C4×C103H(5,𝔽2)11yescharacteristic
320C8×C103—22no—
321C8×C103—22no—
322C8×C103—41no—
323C8×C103—41no—
324C22×C103—42no—
325C22×C103—42no—
326C22×C103—42no—
327C22×C103—81no—
328C22×C103—81no—
329C22×C103—81no—
330C22×C103—81no—
331C22×C103C2×#12111yescharacteristic
332C22×C103D4211yescharacteristic
333C22×C103#55011yescharacteristic
334C22×C103C2×#13711yescharacteristic
335C22×C103C2×#13711yescharacteristic
336C22×C103#57711yescharacteristic
337C22×C103#57811yescharacteristic
338C4×C103—22no—
339C4×C103—22no—
340C4×C103—22no—
341C4×C103—22no—
342C4×C103—42no—
343C4×C103—42no—
344C4×C103—41no—
345C4×C103—42no—
346C4×C103—41no—
347C4×C103—81no—
348C4×C103—81no—
349C4×C103—81no—
350C4×C103—81no—
351C4×C103#53211yescharacteristic
352C4×C103#54011yescharacteristic
353C4×C103D4211yescharacteristic
354C4×C103#54611yescharacteristic
355#25382C10311yesmaximal, characteristic, direct product factor, Sylow
356C2×C103—82no—
357C2×C103#242811yescharacteristic
358C2×C103#303911yescharacteristic
359C2×C103#304611yescharacteristic
360C2×C103#326611yescharacteristic
361C2×C103#327011yescharacteristic
362C2×C103#339811yescharacteristic
363C2×C103#340011yescharacteristic
364C2×#497C2×C10311yescharacteristic
365C2×#464C2×C10311yescharacteristic
366C2×#462C2×C10311yescharacteristic, complemented
367C2×#461C2×C10311yescharacteristic
368#2546C2×C10311yescharacteristic, complemented
369#2367C2×C10311yescharacteristic
370#2056C2×C10311yescharacteristic, complemented
371#2055C2×C10311yescharacteristic
372#2016C2×C10311yescharacteristic, complemented
373#2013C2×C10311yescharacteristic
374#1981C2×C10311yescharacteristic, complemented
375#1940C2×C10311yescharacteristic, complemented
376#1878C2×C10311yescharacteristic, complemented
377#1877C2×C10311yescharacteristic
378#1763C2×C10311yescharacteristic, complemented
379C103#2538211yescharacteristic, direct product factor, Sylow
380C22×Q16C22×C10311yescharacteristic
381C22×Q16C22×C10311yescharacteristic
382C22×Q16C22×C10311yescharacteristic
383C22×SD16C22×C10311yescharacteristic
384C22×SD16C22×C10311yescharacteristic
385C22×SD16C22×C10311yescharacteristic
386C2×C4⋊Q8C22×C10311yescharacteristic
387C2×C4⋊Q8C22×C10311yescharacteristic
388C2×C4⋊Q8C22×C10311yescharacteristic
389C2×#124C22×C10311yescharacteristic
390C2×C4×Q8C22×C10311yescharacteristic
391C2×C4×Q8C22×C10311yescharacteristic
392C2×C4×D4C22×C10311yescharacteristic
393#497—24no—
394#464—24no—
395#462—24no—
396#461—24no—
397C2×C4⋊C8C22×C10311yescharacteristic
398C2×C4⋊C8C22×C10311yescharacteristic
399C2×C4⋊C8C22×C10311yescharacteristic
400C2×#103C22×C10311yescharacteristic
401C2×#103C22×C10311yescharacteristic
402C2×#103C22×C10311yescharacteristic
403C2×#103C22×C10311yescharacteristic
404C2×#103C22×C10311yescharacteristic
405C2×#103C22×C10311yescharacteristic
406C2×#103C22×C10311yescharacteristic
407C2×#102C22×C10311yescharacteristic
408C2×#97C22×C10311yescharacteristic
409#398—21no—
410#398—21no—
411#391C22×C10311yescharacteristic
412#391C22×C10311yescharacteristic
413#391C22×C10311yescharacteristic
414#390C22×C10311yescharacteristic
415#389—21no—
416#389—21no—
417#388—21no—
418#388—21no—
419#385—21no—
420C4×C4⋊C4C22×C10311yescharacteristic
421C4×C4⋊C4C22×C10311yescharacteristic
422C4×C22⋊C4—21no—
423#340C22×C10311yescharacteristic
424#340C22×C10311yescharacteristic
425#336C22×C10311yescharacteristic
426#336C22×C10311yescharacteristic
427C22×Q8C23×C10311yescharacteristic
428C22×Q8C23×C10311yescharacteristic
429C22×Q8C23×C10311yescharacteristic
430C22×Q8C23×C10311yescharacteristic
431C22×D4C23×C10311yescharacteristic
432C23×C4—21no—
433C2×Q16—22no—
434C2×Q16—22no—
435C2×Q16—22no—
436C2×Q16—22no—
437C2×Q16—22no—
438C2×Q16—22no—
439C2×Q16—41no—
440C2×Q16—41no—
441C2×Q16—41no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—22no—
445C2×SD16—22no—
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—41no—
449C2×SD16—41no—
450C2×SD16—41no—
451C22×C8C23×C10311yescharacteristic
452C22×C8C23×C10311yescharacteristic
453C22×C8C23×C10311yescharacteristic
454C22×C8C23×C10311yescharacteristic
455C4⋊Q8—22no—
456C4⋊Q8—22no—
457C4⋊Q8—22no—
458C4⋊Q8—22no—
459C4⋊Q8—41no—
460C4⋊Q8—41no—
461#124—22no—
462#124D4×C10314yes—
463C4×Q8—22no—
464C4×Q8—22no—
465C4×Q8—22no—
466C4×Q8—41no—
467C4×D4—22no—
468C4×D4—41no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4D4×C10311yescharacteristic
478C2×C4⋊C4D4×C10311yescharacteristic
479C2×C4⋊C4C23×C10311yescharacteristic
480C2×C4⋊C4C23×C10311yescharacteristic
481C2×C4⋊C4C23×C10311yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—21no—
490C2×C42C23×C10311yescharacteristic
491C2×C42C23×C10311yescharacteristic
492C2×C42C23×C10311yescharacteristic
493C4⋊C8—22no—
494C4⋊C8—22no—
495C4⋊C8—22no—
496#103—22no—
497#103—22no—
498#103—22no—
499#103—22no—
500#103—41no—
501#103—41no—
502#103D4×C10314yes—
503#102—22no—
504#97—22no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95D4×C10311yescharacteristic
513#95D4×C10311yescharacteristic
514C24—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8C2×D4×C10312yes—
538C2×Q8C2×D4×C10312yes—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4C2×D4×C10312yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—81no—
555C22×C4C2×D4×C10311yescharacteristic
556C22×C4C2×D4×C10311yescharacteristic
557C22×C4C2×D4×C10311yescharacteristic
558C22×C4C2×D4×C10311yescharacteristic
559C22×C4C2×D4×C10311yescharacteristic
560C22×C4C2×D4×C10311yescharacteristic
561C22×C4C24×C10311yescharacteristic
562Q16—44no—
563Q16—44no—
564Q16—44no—
565SD16—44no—
566SD16—44no—
567SD16—44no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8C2×D4×C10312yes—
579C2×C8#41×C10312yes—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4C2×D4×C10312yes—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—81no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—42no—
606C42—42no—
607C42—81no—
608C42C2×D4×C10312yes—
609C42#41×C10312yes—
610C23—22no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23C22×D4×C10311yescharacteristic
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—22no—
622Q8—41no—
623Q8—41no—
624Q8—41no—
625Q8—41no—
626Q8—41no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634D4—22no—
635D4—22no—
636D4—41no—
637D4—41no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—84no—
674C2×C4#121×C10312yes—
675C2×C4#121×C10312yes—
676C2×C4#137×C10312yes—
677C2×C4#137×C10312yes—
678C2×C4C22×D4×C10311yescharacteristic
679C2×C4C22×D4×C10311yescharacteristic
680C2×C4C2×#41×C10311yescharacteristic
681C2×C4C2×#41×C10311yescharacteristic
682C2×C4H(5,𝔽2)×C10311yescharacteristic
683C2×C4H(5,𝔽2)×C10311yescharacteristic
684C8—22no—
685C8—22no—
686C8—41no—
687C8—41no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22C2×#121×C10311yescharacteristic
696C22D42×C10311yescharacteristic
697C22#550×C10311yescharacteristic
698C22C2×#137×C10311yescharacteristic
699C22C2×#137×C10311yescharacteristic
700C22#577×C10311yescharacteristic
701C22#578×C10311yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—41no—
707C4—42no—
708C4—41no—
709C4—42no—
710C4—42no—
711C4—81no—
712C4—81no—
713C4—81no—
714C4—81no—
715C4#532×C10311yescharacteristic
716C4#540×C10311yescharacteristic
717C4D42×C10311yescharacteristic
718C4#546×C10311yescharacteristic
719C2—82no—
720C2C103×#242811yescharacteristic
721C2C103×#303911yescharacteristic
722C2C103×#304611yescharacteristic
723C2C103×#326611yescharacteristic
724C2C103×#327011yescharacteristic
725C2C103×#339811yescharacteristic
726C2C103×#340011yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC22×D4×C103C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C4⋊C4×C103 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#462×C103C2semidirect
5. C103×#2546C2semidirect
7. C103×#2056C2semidirect
9. C103×#2016C2semidirect
11. C103×#1981C2semidirect
12. C103×#1940C2semidirect
13. C103×#1878C2semidirect
15. C103×#1763C2semidirect
355. #25382C103direct (N × H)
366. C2×#462C2×C103semidirect
368. #2546C2×C103semidirect
370. #2056C2×C103semidirect
372. #2016C2×C103semidirect
374. #1981C2×C103semidirect
375. #1940C2×C103semidirect
376. #1878C2×C103semidirect
378. #1763C2×C103semidirect
379. C103#25382direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#497×C1032
C2×#464×C1032
C2×#462×C1032
C2×#461×C1032
C103×#25462
C103×#23672
C103×#20562
C103×#20552
C103×#20162
C103×#20132
C103×#19812
C103×#19402
C103×#18782
C103×#18772
C103×#17632
#25382103